Question

1. A crusher was used to crush a material and the screen analysis of the product is:

Size if aperture (mm)	Mass retained %
6	0
4	26
2	18
0.75	23
0.50	8
0.25	17
0.125	3
pan	5

Calculate the:

1. volume-surface mean diameter
2. arithmetic mean diameter
3. mass mean diameter
4. volume mean diameter.
5. specific surface area (mm²/g) and the total particles/g of  the sample given that the density of the particles is 0.00265 g/mm³, the shape factor and the sphericity are 2 and 0.571,respectively.

2. A spray-dried detergent has the following screen analysis:

Tyler Screen Mesh	Weight fraction retained
14	0.02
20	0.17
28	0.34
35	0.22
48	0.14
65	0.06
100	0.03
pan	0.02

1. Present this information in an undersize cumulative plot.
2. Determine the volume-surface mean and the volume-mean diameters.

Answer 1

avg. size Di	Di^2	Di^3	Di^4	mass fraction Xi	xiDi		Xi/Di	Xi/Di^2	Xi/Di^3		vol surface mean dia
>6				0							0.549267643
5	25	125	625	0.26	1.3		0.052	0.0104	0.00208		arimthmatic mean dia
3	9	27	81	0.18	0.54		0.06	0.02	0.006667		0.071451152
1.375	1.890625	2.599609375	3.574462891	0.23	0.31625		0.167273	0.121653	0.088475		volume mean dia
0.625	0.390625	0.244140625	0.152587891	0.08	0.05		0.128	0.2048	0.32768		0.167445569
0.375	0.140625	0.052734375	0.019775391	0.17	0.06375		0.453333	1.208889	3.223704		mass mean dia
0.1875	0.03515625	0.006591797	0.001235962	0.03	0.005625		0.16	0.853333	4.551111		2.27875
0.0625	0.00390625	0.000244141	1.52588E-05	0.05	0.003125		0.8	12.8	204.8		sp. Surface area
				sum	2.27875		1.820606	15.21908	212.9997		7219.136479